This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.
  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_pelagic 5 1.497782
beta0_pelagic 3 1.411919
beta3_pH 3 1.297780
beta3_pelagic 1 1.284141
beta0_black 1 1.279525
beta2_yellow 4 1.276119
beta1_pH 8 1.260555
beta0_pH 6 1.258919
parameter n badRhat_avg
beta2_pH 13 1.233590
beta2_pelagic 6 1.228693
beta3_yellow 1 1.179085
beta4_pelagic 1 1.165358
beta1_yellow 2 1.145926
beta0_yellow 3 1.134571
tau_beta0_pH 1 1.113793
Table 2. Summary of unconverged parameters by area
afognak CI CSEO EWYKT NG northeast NSEI NSEO PWSI PWSO SSEI SSEO WKMA
beta0_black 1 0 0 0 0 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 1 0 0 0 0 0 0 1 0 1 0
beta0_pH 0 1 1 0 0 1 1 0 0 1 0 1 0
beta0_yellow 0 0 1 0 0 0 0 0 0 1 1 0 0
beta1_pelagic 0 0 1 0 0 0 0 1 1 1 0 1 0
beta1_pH 0 1 1 0 0 1 1 0 1 1 0 1 0
beta1_yellow 0 0 1 0 0 0 0 0 0 0 1 0 0
beta2_pelagic 0 0 1 1 0 0 1 0 1 0 1 1 0
beta2_pH 0 1 1 1 1 1 1 1 1 1 1 1 1
beta2_yellow 0 1 0 0 1 0 0 0 1 1 0 0 0
beta3_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 0 0 0 1 1 0 0 1 0 0 0
beta3_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 0 1 0
tau_beta0_pH 0 1 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.125 0.074 -0.261 -0.128 0.030
mu_bc_H[2] -0.095 0.047 -0.174 -0.098 0.007
mu_bc_H[3] -0.432 0.073 -0.574 -0.432 -0.285
mu_bc_H[4] -0.997 0.191 -1.377 -0.992 -0.635
mu_bc_H[5] 0.903 0.950 -0.198 0.715 3.237
mu_bc_H[6] -2.132 0.334 -2.803 -2.137 -1.471
mu_bc_H[7] -0.456 0.107 -0.674 -0.454 -0.254
mu_bc_H[8] 0.251 0.365 -0.330 0.206 1.083
mu_bc_H[9] -0.297 0.136 -0.564 -0.297 -0.032
mu_bc_H[10] -0.104 0.072 -0.236 -0.107 0.045
mu_bc_H[11] -0.126 0.039 -0.201 -0.126 -0.050
mu_bc_H[12] -0.250 0.108 -0.487 -0.247 -0.044
mu_bc_H[13] -0.130 0.075 -0.279 -0.131 0.022
mu_bc_H[14] -0.305 0.098 -0.510 -0.303 -0.120
mu_bc_H[15] -0.342 0.049 -0.438 -0.343 -0.243
mu_bc_H[16] -0.291 0.383 -0.949 -0.323 0.510
mu_bc_R[1] 1.301 0.148 1.022 1.295 1.602
mu_bc_R[2] 1.457 0.093 1.268 1.457 1.636
mu_bc_R[3] 1.392 0.140 1.108 1.395 1.662
mu_bc_R[4] 0.921 0.208 0.492 0.930 1.302
mu_bc_R[5] 1.185 0.470 0.250 1.197 2.078
mu_bc_R[6] -1.587 0.421 -2.413 -1.581 -0.769
mu_bc_R[7] 0.457 0.205 0.035 0.464 0.839
mu_bc_R[8] 0.564 0.195 0.170 0.567 0.943
mu_bc_R[9] 0.355 0.199 -0.083 0.367 0.712
mu_bc_R[10] 1.307 0.136 1.027 1.309 1.562
mu_bc_R[11] 1.046 0.095 0.858 1.046 1.238
mu_bc_R[12] 0.813 0.204 0.403 0.818 1.206
mu_bc_R[13] 1.027 0.104 0.818 1.029 1.228
mu_bc_R[14] 0.902 0.139 0.620 0.905 1.171
mu_bc_R[15] 0.781 0.110 0.558 0.781 0.991
mu_bc_R[16] 1.096 0.128 0.839 1.093 1.351
tau_pH[1] 4.904 0.781 2.647 5.042 5.997
tau_pH[2] 2.026 0.223 1.616 2.014 2.493
tau_pH[3] 2.099 0.240 1.649 2.097 2.573
beta0_pH[1,1] 0.570 0.195 0.216 0.568 0.948
beta0_pH[2,1] 1.399 0.189 1.011 1.401 1.764
beta0_pH[3,1] 1.452 0.198 1.040 1.460 1.812
beta0_pH[4,1] 1.642 0.326 1.129 1.613 2.806
beta0_pH[5,1] -0.820 0.302 -1.450 -0.809 -0.273
beta0_pH[6,1] -0.716 0.502 -2.067 -0.624 -0.027
beta0_pH[7,1] -0.309 0.470 -1.249 -0.334 0.709
beta0_pH[8,1] -0.654 0.284 -1.395 -0.622 -0.200
beta0_pH[9,1] -0.586 0.295 -1.238 -0.575 -0.040
beta0_pH[10,1] 0.383 0.429 -0.134 0.289 1.642
beta0_pH[11,1] -0.126 0.250 -0.517 -0.139 0.311
beta0_pH[12,1] 0.461 0.202 0.083 0.463 0.848
beta0_pH[13,1] 0.014 0.167 -0.291 0.008 0.362
beta0_pH[14,1] -0.285 0.196 -0.630 -0.297 0.169
beta0_pH[15,1] -0.031 0.187 -0.399 -0.028 0.334
beta0_pH[16,1] -0.416 0.419 -1.592 -0.341 0.200
beta0_pH[1,2] 2.842 0.161 2.514 2.849 3.162
beta0_pH[2,2] 2.894 0.136 2.625 2.894 3.164
beta0_pH[3,2] 3.133 0.161 2.846 3.130 3.456
beta0_pH[4,2] 2.944 0.132 2.675 2.944 3.201
beta0_pH[5,2] 4.855 1.458 2.997 4.555 8.503
beta0_pH[6,2] 3.111 0.206 2.713 3.113 3.508
beta0_pH[7,2] 1.840 0.198 1.443 1.846 2.218
beta0_pH[8,2] 2.870 0.174 2.533 2.867 3.213
beta0_pH[9,2] 3.426 0.222 2.998 3.421 3.864
beta0_pH[10,2] 3.758 0.198 3.382 3.756 4.157
beta0_pH[11,2] -4.845 0.288 -5.419 -4.844 -4.278
beta0_pH[12,2] -4.761 0.378 -5.499 -4.757 -4.044
beta0_pH[13,2] -4.576 0.396 -5.343 -4.586 -3.787
beta0_pH[14,2] -5.569 0.459 -6.602 -5.537 -4.767
beta0_pH[15,2] -4.295 0.336 -4.916 -4.299 -3.620
beta0_pH[16,2] -4.846 0.379 -5.622 -4.838 -4.147
beta0_pH[1,3] 0.006 0.754 -1.744 0.108 1.207
beta0_pH[2,3] 2.194 0.161 1.879 2.199 2.512
beta0_pH[3,3] 2.525 0.152 2.228 2.523 2.827
beta0_pH[4,3] 2.964 0.165 2.645 2.965 3.293
beta0_pH[5,3] 2.118 1.365 0.404 1.835 5.671
beta0_pH[6,3] 0.986 0.497 -0.203 1.043 1.835
beta0_pH[7,3] 0.621 0.169 0.295 0.623 0.957
beta0_pH[8,3] 0.306 0.197 -0.076 0.309 0.685
beta0_pH[9,3] -0.644 0.403 -1.700 -0.600 0.008
beta0_pH[10,3] 0.443 0.409 -0.545 0.504 1.062
beta0_pH[11,3] 0.044 0.512 -0.926 0.058 1.036
beta0_pH[12,3] -0.859 0.408 -1.665 -0.854 -0.144
beta0_pH[13,3] -0.040 0.460 -0.982 -0.040 0.879
beta0_pH[14,3] -0.215 0.315 -0.797 -0.229 0.405
beta0_pH[15,3] -0.695 0.334 -1.352 -0.712 -0.030
beta0_pH[16,3] -0.318 0.337 -0.945 -0.328 0.336
beta1_pH[1,1] 3.055 0.339 2.403 3.045 3.759
beta1_pH[2,1] 2.112 0.302 1.571 2.102 2.722
beta1_pH[3,1] 1.925 0.316 1.333 1.914 2.619
beta1_pH[4,1] 2.322 0.484 1.538 2.298 3.294
beta1_pH[5,1] 2.260 0.359 1.645 2.228 3.050
beta1_pH[6,1] 3.907 1.269 2.191 3.677 7.217
beta1_pH[7,1] 2.230 0.918 0.288 2.283 3.965
beta1_pH[8,1] 4.073 1.118 2.536 3.818 6.932
beta1_pH[9,1] 2.228 0.380 1.484 2.208 3.044
beta1_pH[10,1] 2.189 0.623 0.071 2.316 2.894
beta1_pH[11,1] 3.302 0.278 2.760 3.315 3.767
beta1_pH[12,1] 2.580 0.233 2.110 2.581 3.014
beta1_pH[13,1] 2.960 0.244 2.445 2.965 3.415
beta1_pH[14,1] 3.385 0.249 2.847 3.390 3.848
beta1_pH[15,1] 2.543 0.229 2.114 2.542 2.989
beta1_pH[16,1] 3.982 0.738 2.986 3.837 6.044
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.007 0.091 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.000 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.688 0.328 6.071 6.681 7.346
beta1_pH[12,2] 6.418 0.440 5.598 6.414 7.342
beta1_pH[13,2] 6.967 0.431 6.159 6.959 7.826
beta1_pH[14,2] 7.217 0.485 6.364 7.186 8.306
beta1_pH[15,2] 6.773 0.370 6.030 6.782 7.502
beta1_pH[16,2] 7.448 0.417 6.638 7.448 8.315
beta1_pH[1,3] 4.158 1.657 1.781 3.766 7.781
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.432 3.054 0.828 2.796 11.041
beta1_pH[6,3] 2.948 2.271 0.452 2.621 8.396
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.755 0.348 2.086 2.752 3.442
beta1_pH[9,3] 2.767 0.476 2.009 2.721 3.943
beta1_pH[10,3] 2.934 0.479 2.194 2.878 4.144
beta1_pH[11,3] 2.488 0.611 1.101 2.493 3.692
beta1_pH[12,3] 4.110 0.535 3.197 4.124 5.095
beta1_pH[13,3] 1.615 0.485 0.568 1.615 2.598
beta1_pH[14,3] 2.437 0.419 1.659 2.464 3.190
beta1_pH[15,3] 1.975 0.368 1.248 1.992 2.677
beta1_pH[16,3] 1.712 0.380 0.976 1.718 2.427
beta2_pH[1,1] 0.545 0.680 0.286 0.469 0.887
beta2_pH[2,1] 0.702 0.827 0.247 0.538 2.228
beta2_pH[3,1] 0.827 1.124 0.231 0.577 3.359
beta2_pH[4,1] 0.568 1.168 -1.169 0.456 1.509
beta2_pH[5,1] 1.469 1.021 0.241 1.321 3.842
beta2_pH[6,1] 0.179 0.120 0.074 0.172 0.352
beta2_pH[7,1] 0.029 0.154 0.000 0.000 0.241
beta2_pH[8,1] 0.245 0.106 0.115 0.227 0.462
beta2_pH[9,1] 0.488 0.350 0.200 0.418 1.185
beta2_pH[10,1] 0.466 0.558 -0.877 0.517 1.233
beta2_pH[11,1] 0.845 0.920 0.464 0.734 1.484
beta2_pH[12,1] 1.374 0.995 0.699 1.197 2.676
beta2_pH[13,1] 0.813 1.004 0.411 0.704 1.347
beta2_pH[14,1] 0.990 1.342 0.519 0.804 1.599
beta2_pH[15,1] 0.896 1.034 0.416 0.749 1.767
beta2_pH[16,1] 0.542 1.115 0.155 0.372 1.135
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.045 1.865 -6.846 -1.531 -0.027
beta2_pH[4,2] -1.979 1.866 -6.950 -1.445 -0.031
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.299 4.351 -20.567 -8.288 -3.925
beta2_pH[12,2] -7.897 5.056 -20.379 -7.027 -1.046
beta2_pH[13,2] -7.753 5.022 -20.374 -6.728 -1.684
beta2_pH[14,2] -8.421 4.707 -20.416 -7.358 -2.473
beta2_pH[15,2] -9.189 4.460 -20.936 -8.207 -3.835
beta2_pH[16,2] -9.396 4.331 -20.281 -8.354 -4.056
beta2_pH[1,3] 0.325 0.547 0.101 0.222 1.119
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.827 6.403 -0.315 7.846 23.704
beta2_pH[6,3] 8.946 6.290 0.134 7.992 23.319
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 9.875 5.768 1.653 8.795 23.433
beta2_pH[9,3] 8.837 6.342 0.476 7.605 23.471
beta2_pH[10,3] 8.331 6.490 0.483 7.279 23.871
beta2_pH[11,3] -3.012 3.101 -12.679 -1.925 -0.531
beta2_pH[12,3] -2.873 2.863 -11.527 -1.943 -0.916
beta2_pH[13,3] -3.011 3.466 -12.527 -2.162 2.275
beta2_pH[14,3] -3.403 3.050 -12.223 -2.363 -0.880
beta2_pH[15,3] -3.622 3.090 -12.647 -2.566 -0.926
beta2_pH[16,3] -3.605 3.125 -12.534 -2.521 -0.852
beta3_pH[1,1] 35.999 0.926 34.333 35.963 37.839
beta3_pH[2,1] 33.662 1.290 31.490 33.538 36.690
beta3_pH[3,1] 33.581 1.061 31.538 33.555 35.814
beta3_pH[4,1] 33.438 2.789 21.047 33.704 36.563
beta3_pH[5,1] 27.782 1.204 26.482 27.506 31.246
beta3_pH[6,1] 38.475 3.484 32.514 38.311 45.082
beta3_pH[7,1] 30.744 7.911 18.635 30.486 44.968
beta3_pH[8,1] 40.131 2.496 35.531 39.904 45.185
beta3_pH[9,1] 30.676 1.433 28.054 30.611 33.665
beta3_pH[10,1] 31.972 3.728 18.800 32.678 35.070
beta3_pH[11,1] 30.206 0.541 29.278 30.185 31.199
beta3_pH[12,1] 30.124 0.425 29.288 30.122 30.934
beta3_pH[13,1] 33.170 0.607 32.050 33.152 34.439
beta3_pH[14,1] 32.063 0.536 31.135 32.032 33.194
beta3_pH[15,1] 31.207 0.710 29.923 31.175 32.639
beta3_pH[16,1] 31.967 1.166 30.259 31.819 34.550
beta3_pH[1,2] 29.867 8.046 18.466 28.638 44.854
beta3_pH[2,2] 30.023 7.949 18.474 29.048 44.757
beta3_pH[3,2] 29.952 8.082 18.380 28.811 44.884
beta3_pH[4,2] 29.745 7.914 18.424 28.734 44.966
beta3_pH[5,2] 30.226 8.014 18.502 29.271 45.020
beta3_pH[6,2] 29.870 7.918 18.444 28.814 44.793
beta3_pH[7,2] 29.910 7.948 18.466 29.153 44.791
beta3_pH[8,2] 29.913 7.903 18.459 28.995 44.807
beta3_pH[9,2] 29.986 8.081 18.456 29.098 44.923
beta3_pH[10,2] 29.813 7.992 18.401 28.831 44.916
beta3_pH[11,2] 43.401 0.180 43.117 43.379 43.771
beta3_pH[12,2] 43.195 0.200 42.922 43.142 43.738
beta3_pH[13,2] 43.863 0.147 43.469 43.902 44.041
beta3_pH[14,2] 43.293 0.204 43.043 43.236 43.811
beta3_pH[15,2] 43.405 0.192 43.102 43.385 43.810
beta3_pH[16,2] 43.490 0.187 43.159 43.486 43.841
beta3_pH[1,3] 38.472 3.194 32.061 38.463 44.936
beta3_pH[2,3] 30.475 7.952 18.512 29.923 44.868
beta3_pH[3,3] 30.240 8.156 18.428 29.445 45.047
beta3_pH[4,3] 30.273 8.056 18.514 29.603 45.040
beta3_pH[5,3] 36.744 3.864 31.237 36.126 45.053
beta3_pH[6,3] 40.301 3.586 31.752 40.764 45.603
beta3_pH[7,3] 38.088 4.327 31.311 37.849 45.538
beta3_pH[8,3] 41.485 0.262 41.052 41.482 41.940
beta3_pH[9,3] 33.443 0.608 31.545 33.545 34.325
beta3_pH[10,3] 35.787 0.823 33.377 36.001 36.833
beta3_pH[11,3] 41.529 1.005 39.564 41.552 43.509
beta3_pH[12,3] 41.719 0.420 40.955 41.744 42.525
beta3_pH[13,3] 41.995 3.048 30.651 42.707 45.207
beta3_pH[14,3] 41.046 0.741 39.711 41.094 42.231
beta3_pH[15,3] 42.729 0.821 41.164 42.845 43.862
beta3_pH[16,3] 42.808 0.933 40.820 42.983 44.128
beta0_pelagic[1] 2.221 0.132 1.966 2.221 2.480
beta0_pelagic[2] 1.505 0.120 1.272 1.506 1.745
beta0_pelagic[3] 0.012 0.390 -0.954 0.074 0.633
beta0_pelagic[4] -0.057 0.570 -1.368 -0.010 0.836
beta0_pelagic[5] 1.190 0.253 0.686 1.190 1.694
beta0_pelagic[6] 1.453 0.274 0.872 1.475 1.947
beta0_pelagic[7] 1.583 0.210 1.181 1.576 2.028
beta0_pelagic[8] 1.762 0.217 1.348 1.753 2.208
beta0_pelagic[9] 2.486 0.317 1.860 2.494 3.065
beta0_pelagic[10] 2.529 0.208 2.089 2.535 2.918
beta0_pelagic[11] -0.462 0.497 -1.527 -0.433 0.431
beta0_pelagic[12] 1.683 0.145 1.399 1.686 1.971
beta0_pelagic[13] 0.224 0.279 -0.637 0.269 0.634
beta0_pelagic[14] -0.156 0.299 -0.916 -0.126 0.323
beta0_pelagic[15] -0.267 0.141 -0.535 -0.268 0.021
beta0_pelagic[16] 0.248 0.257 -0.335 0.289 0.635
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.319 0.658 0.380 1.181 2.966
beta1_pelagic[4] 1.343 0.629 0.263 1.269 2.691
beta1_pelagic[5] -0.071 0.319 -0.701 -0.069 0.538
beta1_pelagic[6] -0.082 0.461 -0.866 -0.127 0.752
beta1_pelagic[7] -0.009 0.291 -0.554 -0.013 0.574
beta1_pelagic[8] -0.012 0.287 -0.585 -0.018 0.556
beta1_pelagic[9] 0.201 0.490 -0.787 0.318 0.960
beta1_pelagic[10] 0.057 0.273 -0.480 0.056 0.595
beta1_pelagic[11] 4.937 1.225 2.822 4.958 7.407
beta1_pelagic[12] 2.824 0.360 2.189 2.802 3.630
beta1_pelagic[13] 3.281 0.817 1.871 3.291 4.871
beta1_pelagic[14] 4.816 0.957 3.201 4.723 6.843
beta1_pelagic[15] 2.954 0.280 2.338 2.958 3.459
beta1_pelagic[16] 3.814 0.970 2.716 3.470 6.444
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 1.057 2.733 0.054 0.249 9.528
beta2_pelagic[4] 1.757 3.780 0.068 0.479 15.552
beta2_pelagic[5] -0.042 0.679 -1.537 -0.027 1.375
beta2_pelagic[6] -0.082 0.701 -1.476 -0.122 1.394
beta2_pelagic[7] 0.014 0.639 -1.342 0.003 1.356
beta2_pelagic[8] 0.189 0.625 -0.910 0.090 1.594
beta2_pelagic[9] 0.173 0.699 -1.404 0.258 1.493
beta2_pelagic[10] 0.056 0.632 -1.237 0.034 1.494
beta2_pelagic[11] 0.205 0.185 0.094 0.157 0.660
beta2_pelagic[12] 5.136 4.604 0.740 3.719 18.113
beta2_pelagic[13] 0.610 1.046 0.133 0.368 2.688
beta2_pelagic[14] 0.282 0.107 0.142 0.263 0.572
beta2_pelagic[15] 5.427 4.587 1.090 4.088 18.558
beta2_pelagic[16] 3.614 4.906 0.208 0.968 17.302
beta3_pelagic[1] 29.892 7.946 18.516 28.993 45.073
beta3_pelagic[2] 29.850 7.958 18.476 28.521 44.856
beta3_pelagic[3] 31.064 5.559 20.996 30.358 43.377
beta3_pelagic[4] 25.284 4.220 19.401 24.756 37.721
beta3_pelagic[5] 29.955 8.190 18.463 28.564 45.233
beta3_pelagic[6] 31.706 6.716 19.042 31.643 44.417
beta3_pelagic[7] 29.820 7.919 18.509 28.741 44.931
beta3_pelagic[8] 29.320 7.964 18.459 27.755 44.912
beta3_pelagic[9] 31.010 6.040 19.438 31.093 43.594
beta3_pelagic[10] 29.704 8.272 18.410 28.209 45.156
beta3_pelagic[11] 42.218 2.843 33.735 42.712 45.840
beta3_pelagic[12] 43.479 0.318 42.961 43.455 44.153
beta3_pelagic[13] 43.130 1.444 40.034 43.133 45.761
beta3_pelagic[14] 42.958 1.585 39.640 42.940 45.770
beta3_pelagic[15] 43.139 0.270 42.537 43.149 43.665
beta3_pelagic[16] 43.091 0.959 40.531 43.196 45.100
mu_beta0_pelagic[1] 0.857 0.969 -1.255 0.889 2.773
mu_beta0_pelagic[2] 1.805 0.399 0.972 1.815 2.589
mu_beta0_pelagic[3] 0.203 0.501 -0.823 0.220 1.138
tau_beta0_pelagic[1] 0.611 0.649 0.054 0.410 2.377
tau_beta0_pelagic[2] 2.621 2.553 0.249 1.930 8.923
tau_beta0_pelagic[3] 1.285 1.015 0.155 1.012 3.998
beta0_yellow[1] -0.536 0.188 -0.959 -0.522 -0.218
beta0_yellow[2] 0.493 0.153 0.179 0.497 0.787
beta0_yellow[3] -0.327 0.183 -0.712 -0.317 0.002
beta0_yellow[4] 0.782 0.353 -0.231 0.858 1.209
beta0_yellow[5] -0.281 0.356 -0.981 -0.286 0.436
beta0_yellow[6] 1.118 0.163 0.808 1.115 1.441
beta0_yellow[7] 0.984 0.160 0.680 0.979 1.315
beta0_yellow[8] 1.010 0.155 0.701 1.012 1.315
beta0_yellow[9] 0.658 0.159 0.348 0.658 0.978
beta0_yellow[10] 0.581 0.142 0.304 0.582 0.858
beta0_yellow[11] -1.937 0.447 -2.799 -1.961 -0.958
beta0_yellow[12] -3.690 0.412 -4.520 -3.681 -2.912
beta0_yellow[13] -3.729 0.538 -4.969 -3.678 -2.819
beta0_yellow[14] -2.104 0.501 -3.024 -2.127 -1.074
beta0_yellow[15] -2.833 0.456 -3.870 -2.774 -2.062
beta0_yellow[16] -2.347 0.452 -3.204 -2.357 -1.428
beta1_yellow[1] 0.803 1.063 0.008 0.641 2.601
beta1_yellow[2] 1.075 0.314 0.609 1.045 1.765
beta1_yellow[3] 0.725 0.266 0.243 0.703 1.315
beta1_yellow[4] 1.485 0.850 0.661 1.224 4.029
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.094 0.465 1.145 2.128 2.905
beta1_yellow[12] 2.481 0.424 1.669 2.464 3.359
beta1_yellow[13] 2.845 0.536 1.952 2.783 4.131
beta1_yellow[14] 2.178 0.515 1.127 2.191 3.107
beta1_yellow[15] 2.073 0.456 1.280 2.030 3.127
beta1_yellow[16] 2.107 0.461 1.118 2.133 2.955
beta2_yellow[1] -2.883 2.394 -8.701 -2.337 -0.029
beta2_yellow[2] -2.740 1.985 -6.285 -2.305 -0.205
beta2_yellow[3] -2.441 2.032 -7.648 -1.922 -0.142
beta2_yellow[4] -2.003 2.034 -6.486 -1.122 -0.085
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.816 2.712 -11.296 -4.322 -1.121
beta2_yellow[12] -5.205 2.850 -12.500 -4.583 -1.416
beta2_yellow[13] -4.860 2.601 -11.555 -4.268 -1.463
beta2_yellow[14] -5.066 3.027 -12.576 -4.457 -0.746
beta2_yellow[15] -4.586 2.872 -11.935 -3.872 -1.048
beta2_yellow[16] -5.171 2.808 -12.223 -4.596 -1.376
beta3_yellow[1] 25.631 6.980 18.260 22.624 43.665
beta3_yellow[2] 29.130 1.836 25.262 28.947 32.886
beta3_yellow[3] 32.967 2.921 25.973 32.967 39.054
beta3_yellow[4] 29.228 4.006 20.785 28.250 36.938
beta3_yellow[5] 29.975 8.021 18.416 29.115 44.949
beta3_yellow[6] 29.732 7.941 18.403 28.739 44.773
beta3_yellow[7] 30.165 7.909 18.474 29.414 44.963
beta3_yellow[8] 29.903 7.925 18.484 28.979 44.862
beta3_yellow[9] 30.032 7.917 18.481 29.129 44.834
beta3_yellow[10] 30.613 8.104 18.531 30.027 45.143
beta3_yellow[11] 45.220 0.850 43.720 45.369 45.970
beta3_yellow[12] 43.311 0.382 42.554 43.285 44.074
beta3_yellow[13] 44.864 0.408 43.967 44.945 45.552
beta3_yellow[14] 44.249 0.964 43.053 44.242 45.863
beta3_yellow[15] 45.132 0.530 44.139 45.103 45.970
beta3_yellow[16] 44.555 0.648 43.401 44.530 45.824
mu_beta0_yellow[1] 0.086 0.554 -1.059 0.076 1.248
mu_beta0_yellow[2] 0.648 0.327 -0.050 0.672 1.250
mu_beta0_yellow[3] -2.412 0.638 -3.409 -2.513 -0.891
tau_beta0_yellow[1] 1.896 2.502 0.099 1.212 7.863
tau_beta0_yellow[2] 3.583 4.345 0.327 2.396 13.709
tau_beta0_yellow[3] 1.366 2.048 0.098 0.877 5.236
beta0_black[1] -0.075 0.156 -0.365 -0.076 0.233
beta0_black[2] 1.915 0.131 1.666 1.914 2.176
beta0_black[3] 1.317 0.136 1.047 1.319 1.579
beta0_black[4] 2.428 0.136 2.163 2.425 2.692
beta0_black[5] 4.598 2.078 1.860 4.127 10.090
beta0_black[6] 4.603 1.917 2.206 4.130 9.699
beta0_black[7] 3.772 1.874 1.553 3.294 8.830
beta0_black[8] 1.022 0.244 0.560 1.021 1.519
beta0_black[9] 2.595 0.234 2.152 2.590 3.059
beta0_black[10] 1.458 0.134 1.190 1.454 1.723
beta0_black[11] 3.483 0.156 3.173 3.481 3.788
beta0_black[12] 4.869 0.171 4.520 4.867 5.198
beta0_black[13] -0.113 0.247 -0.619 -0.108 0.348
beta0_black[14] 2.853 0.156 2.539 2.854 3.163
beta0_black[15] 1.296 0.155 0.978 1.298 1.594
beta0_black[16] 4.278 0.159 3.962 4.279 4.583
beta2_black[1] 7.693 10.039 0.571 3.384 40.092
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.796 1.508 -5.985 -1.312 -0.295
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.761 1.132 39.776 41.910 43.224
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.115 0.986 36.788 39.251 40.551
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.257 0.195 -0.626 -0.257 0.126
beta4_black[2] 0.237 0.190 -0.129 0.236 0.614
beta4_black[3] -0.935 0.199 -1.315 -0.932 -0.540
beta4_black[4] 0.425 0.221 -0.006 0.426 0.847
beta4_black[5] 0.558 1.270 -1.328 0.352 3.764
beta4_black[6] 0.533 1.297 -1.360 0.301 3.735
beta4_black[7] 0.434 1.238 -1.475 0.244 3.222
beta4_black[8] -0.306 0.336 -0.995 -0.303 0.321
beta4_black[9] 0.867 0.802 -0.270 0.710 2.877
beta4_black[10] 0.049 0.186 -0.315 0.049 0.407
beta4_black[11] -0.696 0.217 -1.125 -0.696 -0.270
beta4_black[12] 0.171 0.320 -0.438 0.163 0.828
beta4_black[13] -1.187 0.226 -1.634 -1.183 -0.749
beta4_black[14] -0.178 0.229 -0.624 -0.184 0.279
beta4_black[15] -0.892 0.215 -1.315 -0.886 -0.477
beta4_black[16] -0.593 0.224 -1.034 -0.589 -0.163
mu_beta0_black[1] 1.255 0.881 -0.760 1.304 2.935
mu_beta0_black[2] 2.689 1.048 0.735 2.599 4.963
mu_beta0_black[3] 2.494 1.001 0.297 2.547 4.326
tau_beta0_black[1] 0.636 0.581 0.057 0.458 2.182
tau_beta0_black[2] 0.472 0.756 0.047 0.244 2.347
tau_beta0_black[3] 0.235 0.154 0.051 0.197 0.626
beta0_dsr[11] -2.906 0.273 -3.447 -2.905 -2.371
beta0_dsr[12] 4.559 0.292 3.991 4.556 5.126
beta0_dsr[13] -1.366 0.344 -1.985 -1.352 -0.789
beta0_dsr[14] -3.688 0.524 -4.730 -3.674 -2.696
beta0_dsr[15] -1.957 0.284 -2.506 -1.954 -1.400
beta0_dsr[16] -3.014 0.362 -3.731 -3.009 -2.304
beta1_dsr[11] 4.834 0.292 4.249 4.838 5.414
beta1_dsr[12] 8.367 36.554 2.278 5.126 23.079
beta1_dsr[13] 2.873 0.395 2.277 2.851 3.546
beta1_dsr[14] 6.352 0.552 5.313 6.328 7.493
beta1_dsr[15] 3.353 0.288 2.785 3.355 3.908
beta1_dsr[16] 5.825 0.380 5.082 5.824 6.577
beta2_dsr[11] -8.382 2.348 -13.729 -8.092 -4.648
beta2_dsr[12] -7.178 2.753 -13.140 -6.980 -2.314
beta2_dsr[13] -6.682 2.865 -12.850 -6.427 -1.604
beta2_dsr[14] -6.260 2.744 -12.116 -6.022 -1.794
beta2_dsr[15] -7.964 2.535 -13.896 -7.688 -4.033
beta2_dsr[16] -8.079 2.471 -13.623 -7.755 -4.257
beta3_dsr[11] 43.487 0.153 43.207 43.485 43.781
beta3_dsr[12] 33.972 0.831 32.112 34.114 34.809
beta3_dsr[13] 43.259 0.313 42.849 43.190 43.883
beta3_dsr[14] 43.356 0.242 43.078 43.283 43.963
beta3_dsr[15] 43.510 0.190 43.160 43.509 43.856
beta3_dsr[16] 43.441 0.161 43.164 43.433 43.764
beta4_dsr[11] 0.594 0.220 0.178 0.589 1.025
beta4_dsr[12] 0.244 0.434 -0.655 0.252 1.078
beta4_dsr[13] -0.161 0.218 -0.581 -0.159 0.266
beta4_dsr[14] 0.150 0.249 -0.354 0.153 0.617
beta4_dsr[15] 0.725 0.206 0.321 0.725 1.148
beta4_dsr[16] 0.151 0.234 -0.306 0.152 0.610
beta0_slope[11] -1.847 0.146 -2.139 -1.845 -1.572
beta0_slope[12] -4.479 0.258 -5.007 -4.473 -4.009
beta0_slope[13] -1.355 0.187 -1.798 -1.342 -1.034
beta0_slope[14] -2.670 0.163 -2.994 -2.668 -2.351
beta0_slope[15] -1.344 0.144 -1.624 -1.348 -1.064
beta0_slope[16] -2.735 0.155 -3.036 -2.736 -2.444
beta1_slope[11] 4.487 0.224 4.057 4.489 4.929
beta1_slope[12] 3.989 0.455 3.086 3.987 4.884
beta1_slope[13] 2.738 0.464 2.217 2.651 4.184
beta1_slope[14] 6.304 0.419 5.505 6.307 7.143
beta1_slope[15] 3.015 0.204 2.624 3.016 3.410
beta1_slope[16] 5.276 0.279 4.726 5.279 5.805
beta2_slope[11] 8.766 2.383 5.167 8.337 14.287
beta2_slope[12] 6.614 2.913 1.218 6.586 12.869
beta2_slope[13] 5.111 2.996 0.371 4.952 11.091
beta2_slope[14] 6.288 2.499 2.207 6.118 11.773
beta2_slope[15] 8.238 2.373 4.512 7.848 13.873
beta2_slope[16] 7.758 2.322 4.307 7.438 13.240
beta3_slope[11] 43.461 0.136 43.214 43.452 43.732
beta3_slope[12] 43.350 0.274 42.905 43.313 43.904
beta3_slope[13] 43.449 0.402 42.893 43.391 44.066
beta3_slope[14] 43.269 0.135 43.094 43.237 43.602
beta3_slope[15] 43.494 0.162 43.193 43.491 43.794
beta3_slope[16] 43.374 0.143 43.147 43.354 43.700
beta4_slope[11] -0.732 0.164 -1.059 -0.730 -0.407
beta4_slope[12] -1.163 0.460 -2.165 -1.129 -0.374
beta4_slope[13] 0.090 0.163 -0.226 0.091 0.408
beta4_slope[14] -0.090 0.195 -0.472 -0.095 0.306
beta4_slope[15] -0.763 0.158 -1.075 -0.760 -0.464
beta4_slope[16] -0.160 0.173 -0.498 -0.161 0.171
sigma_H[1] 0.200 0.054 0.103 0.198 0.314
sigma_H[2] 0.172 0.031 0.118 0.170 0.239
sigma_H[3] 0.197 0.044 0.119 0.195 0.289
sigma_H[4] 0.419 0.079 0.290 0.411 0.593
sigma_H[5] 0.993 0.205 0.615 0.981 1.408
sigma_H[6] 0.384 0.206 0.030 0.376 0.817
sigma_H[7] 0.309 0.064 0.210 0.300 0.458
sigma_H[8] 0.418 0.088 0.281 0.409 0.614
sigma_H[9] 0.521 0.122 0.327 0.508 0.787
sigma_H[10] 0.215 0.043 0.139 0.213 0.308
sigma_H[11] 0.277 0.046 0.200 0.273 0.378
sigma_H[12] 0.437 0.164 0.206 0.415 0.767
sigma_H[13] 0.216 0.038 0.152 0.212 0.300
sigma_H[14] 0.508 0.094 0.343 0.501 0.705
sigma_H[15] 0.247 0.039 0.180 0.244 0.332
sigma_H[16] 0.227 0.045 0.152 0.223 0.328
lambda_H[1] 3.186 3.945 0.161 1.873 13.649
lambda_H[2] 8.292 8.037 0.803 5.876 29.702
lambda_H[3] 6.125 9.439 0.275 3.165 30.183
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.722 7.788 0.032 1.046 25.164
lambda_H[6] 7.694 15.046 0.009 0.951 50.845
lambda_H[7] 0.013 0.009 0.002 0.011 0.035
lambda_H[8] 8.149 9.805 0.111 4.636 35.178
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.321 0.800 0.032 0.199 1.114
lambda_H[11] 0.280 0.416 0.012 0.134 1.335
lambda_H[12] 4.764 5.743 0.200 2.828 21.873
lambda_H[13] 3.422 3.135 0.209 2.560 11.649
lambda_H[14] 3.317 4.122 0.243 2.035 14.666
lambda_H[15] 0.026 0.048 0.003 0.017 0.099
lambda_H[16] 0.901 1.277 0.048 0.474 4.330
mu_lambda_H[1] 4.379 1.874 1.253 4.219 8.400
mu_lambda_H[2] 3.878 1.947 0.633 3.767 8.026
mu_lambda_H[3] 3.539 1.826 0.824 3.269 7.659
sigma_lambda_H[1] 8.687 4.234 2.050 8.135 18.003
sigma_lambda_H[2] 8.458 4.705 1.037 7.861 18.244
sigma_lambda_H[3] 6.258 3.878 1.037 5.452 15.943
beta_H[1,1] 6.957 1.062 4.361 7.109 8.612
beta_H[2,1] 9.874 0.489 8.800 9.892 10.799
beta_H[3,1] 8.011 0.804 6.129 8.102 9.289
beta_H[4,1] 9.477 7.781 -6.178 9.698 24.430
beta_H[5,1] 0.125 2.352 -4.927 0.302 4.230
beta_H[6,1] 3.114 3.885 -6.753 4.464 7.559
beta_H[7,1] 0.457 5.931 -12.277 0.922 11.161
beta_H[8,1] 1.304 3.573 -2.228 1.229 3.423
beta_H[9,1] 12.896 5.772 1.162 12.783 24.348
beta_H[10,1] 7.051 1.710 3.483 7.112 10.298
beta_H[11,1] 5.231 3.472 -2.602 6.006 9.966
beta_H[12,1] 2.595 1.120 0.787 2.526 4.909
beta_H[13,1] 9.025 1.043 6.814 9.131 10.536
beta_H[14,1] 2.204 0.997 0.104 2.207 4.225
beta_H[15,1] -6.012 3.850 -12.835 -6.290 2.583
beta_H[16,1] 3.431 2.584 -0.766 3.067 10.125
beta_H[1,2] 7.904 0.239 7.421 7.909 8.352
beta_H[2,2] 10.024 0.139 9.750 10.021 10.297
beta_H[3,2] 8.950 0.200 8.549 8.948 9.335
beta_H[4,2] 3.553 1.484 0.785 3.453 6.700
beta_H[5,2] 1.957 0.976 -0.007 1.987 3.786
beta_H[6,2] 5.705 1.031 3.218 5.869 7.316
beta_H[7,2] 2.652 1.127 0.716 2.549 5.085
beta_H[8,2] 3.006 1.029 1.404 3.148 4.214
beta_H[9,2] 3.514 1.089 1.448 3.486 5.794
beta_H[10,2] 8.190 0.347 7.498 8.203 8.871
beta_H[11,2] 9.756 0.627 8.832 9.636 11.166
beta_H[12,2] 3.942 0.383 3.235 3.936 4.698
beta_H[13,2] 9.119 0.263 8.656 9.109 9.640
beta_H[14,2] 4.026 0.358 3.348 4.017 4.780
beta_H[15,2] 11.340 0.703 9.850 11.393 12.628
beta_H[16,2] 4.548 0.794 3.023 4.544 6.103
beta_H[1,3] 8.452 0.242 8.012 8.444 8.959
beta_H[2,3] 10.064 0.119 9.825 10.062 10.300
beta_H[3,3] 9.611 0.166 9.290 9.609 9.946
beta_H[4,3] -2.480 0.884 -4.195 -2.477 -0.696
beta_H[5,3] 3.849 0.620 2.595 3.844 5.066
beta_H[6,3] 7.962 1.192 6.320 7.613 10.528
beta_H[7,3] -2.762 0.670 -4.091 -2.755 -1.469
beta_H[8,3] 5.240 0.470 4.654 5.184 6.171
beta_H[9,3] -2.831 0.728 -4.264 -2.827 -1.425
beta_H[10,3] 8.700 0.283 8.141 8.695 9.285
beta_H[11,3] 8.547 0.283 7.925 8.576 9.033
beta_H[12,3] 5.253 0.321 4.510 5.290 5.763
beta_H[13,3] 8.837 0.177 8.474 8.841 9.172
beta_H[14,3] 5.720 0.280 5.116 5.739 6.221
beta_H[15,3] 10.374 0.323 9.758 10.364 11.008
beta_H[16,3] 6.319 0.616 4.893 6.383 7.305
beta_H[1,4] 8.264 0.175 7.895 8.277 8.575
beta_H[2,4] 10.127 0.123 9.868 10.133 10.344
beta_H[3,4] 10.112 0.165 9.749 10.125 10.408
beta_H[4,4] 11.799 0.440 10.915 11.805 12.648
beta_H[5,4] 5.516 0.758 4.295 5.429 7.338
beta_H[6,4] 7.043 0.878 5.056 7.288 8.256
beta_H[7,4] 8.260 0.355 7.551 8.257 8.942
beta_H[8,4] 6.708 0.236 6.256 6.717 7.117
beta_H[9,4] 7.222 0.488 6.277 7.216 8.216
beta_H[10,4] 7.750 0.242 7.309 7.741 8.246
beta_H[11,4] 9.394 0.197 9.008 9.394 9.776
beta_H[12,4] 7.136 0.210 6.755 7.132 7.561
beta_H[13,4] 9.033 0.139 8.750 9.036 9.298
beta_H[14,4] 7.737 0.215 7.319 7.738 8.165
beta_H[15,4] 9.469 0.230 9.022 9.469 9.924
beta_H[16,4] 9.346 0.243 8.917 9.329 9.858
beta_H[1,5] 8.987 0.144 8.699 8.990 9.271
beta_H[2,5] 10.784 0.096 10.603 10.780 10.982
beta_H[3,5] 10.920 0.170 10.613 10.911 11.261
beta_H[4,5] 8.392 0.455 7.519 8.389 9.324
beta_H[5,5] 5.412 0.577 4.075 5.468 6.399
beta_H[6,5] 8.741 0.644 7.798 8.595 10.281
beta_H[7,5] 6.748 0.343 6.083 6.739 7.440
beta_H[8,5] 8.216 0.212 7.869 8.201 8.629
beta_H[9,5] 8.199 0.474 7.219 8.209 9.119
beta_H[10,5] 10.080 0.232 9.602 10.074 10.516
beta_H[11,5] 11.505 0.229 11.046 11.512 11.942
beta_H[12,5] 8.477 0.197 8.101 8.472 8.882
beta_H[13,5] 10.005 0.128 9.751 10.003 10.252
beta_H[14,5] 9.197 0.226 8.779 9.189 9.652
beta_H[15,5] 11.167 0.247 10.688 11.168 11.663
beta_H[16,5] 9.925 0.182 9.551 9.932 10.258
beta_H[1,6] 10.181 0.187 9.857 10.166 10.584
beta_H[2,6] 11.512 0.109 11.297 11.511 11.726
beta_H[3,6] 10.809 0.162 10.447 10.817 11.104
beta_H[4,6] 12.893 0.814 11.268 12.892 14.472
beta_H[5,6] 5.890 0.608 4.759 5.877 7.105
beta_H[6,6] 8.764 0.644 7.118 8.877 9.728
beta_H[7,6] 9.861 0.572 8.738 9.862 10.951
beta_H[8,6] 9.523 0.278 9.019 9.539 9.979
beta_H[9,6] 8.478 0.786 6.897 8.469 10.046
beta_H[10,6] 9.497 0.327 8.791 9.533 10.055
beta_H[11,6] 10.827 0.350 10.059 10.857 11.448
beta_H[12,6] 9.372 0.244 8.918 9.369 9.880
beta_H[13,6] 11.045 0.165 10.764 11.040 11.376
beta_H[14,6] 9.828 0.288 9.236 9.829 10.387
beta_H[15,6] 10.833 0.431 9.960 10.844 11.643
beta_H[16,6] 10.553 0.236 10.043 10.558 11.024
beta_H[1,7] 10.913 0.834 8.894 11.006 12.282
beta_H[2,7] 12.206 0.433 11.323 12.217 13.039
beta_H[3,7] 10.544 0.669 9.089 10.597 11.678
beta_H[4,7] 2.497 4.153 -5.518 2.487 10.803
beta_H[5,7] 6.431 1.882 3.045 6.362 10.713
beta_H[6,7] 9.568 2.319 5.115 9.531 15.465
beta_H[7,7] 10.499 2.852 5.024 10.517 16.277
beta_H[8,7] 10.976 1.002 9.438 10.923 12.702
beta_H[9,7] 4.485 3.978 -3.315 4.460 12.535
beta_H[10,7] 9.876 1.481 7.278 9.774 13.039
beta_H[11,7] 10.920 1.689 7.769 10.799 14.721
beta_H[12,7] 9.998 0.942 7.907 10.095 11.516
beta_H[13,7] 11.658 0.767 9.919 11.732 12.862
beta_H[14,7] 10.423 0.955 8.463 10.462 12.115
beta_H[15,7] 12.011 2.221 7.695 11.979 16.325
beta_H[16,7] 12.266 1.225 10.217 12.084 15.078
beta0_H[1] 8.628 13.046 -17.979 8.789 33.693
beta0_H[2] 10.682 6.275 -2.276 10.642 23.900
beta0_H[3] 9.906 9.871 -8.841 9.942 29.972
beta0_H[4] 1.140 185.948 -368.783 4.675 372.957
beta0_H[5] 4.132 25.561 -42.633 4.255 55.696
beta0_H[6] 6.638 48.679 -106.279 7.636 103.062
beta0_H[7] 5.663 134.506 -271.995 9.504 275.221
beta0_H[8] 6.608 34.041 -15.903 6.443 33.009
beta0_H[9] 5.600 121.142 -244.753 7.095 255.308
beta0_H[10] 8.515 33.000 -61.608 8.754 76.597
beta0_H[11] 9.308 47.430 -85.364 9.377 109.616
beta0_H[12] 6.995 11.553 -15.339 7.167 29.879
beta0_H[13] 9.711 11.707 -11.632 9.598 31.071
beta0_H[14] 7.027 11.940 -17.013 7.041 29.944
beta0_H[15] 9.076 102.924 -194.945 6.917 217.362
beta0_H[16] 8.361 25.482 -43.926 7.920 62.713